Adaptive dynamic surface control of a class of pure feedback systems preceded by generalized P‐I hysteresis

Abstract In this paper, an adaptive dynamic surface control is proposed for a class of completely non‐affine nonlinear systems preceded by the generalized Prandtl–Ishlinskii (P‐I) hysteresis, in which the hysteresis input function is also non‐affine with respect to the control input. Instead of the mean value theorem widely used in existing literature, new nonlinear functions are introduced, leading to the removal of the assumption caused by the mean value theorem. Moreover, no constraint is imposed on the bound of the P‐I hysteresis density function. Then, the filtered signals are constructed to address the algebraic loop problem and the complexity explosion inherent in backstepping method. Based on the filtered signals, the adaptive dynamic surface control is developed, which can ensure the transient tracking performance.